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Revise Cover Letter PhD

Hello,
I am an Italiant student, I finished my master in Barcelona and I would like to join a PhD program in Amsterdam. In order to this I need to write a cover letter but I don't know anyone that can correct it. So if there is some volunteer I would be very greatful to him.
Thank in advance you for your kind help,

Tommaso

Dear Professor **** ****,
I am writing you to apply for the PhD at *****. I graduated in Philosophy in 2010 from the University of ****. During my studies I soon became interested in logic and philosophy of language, in particular it fascinated me the connection between propositional logics and certain classes of algebras.

To deepen the study of such connection in September 2010 I decided to join the Master of Pure and Applied Logic in Barcelona. This two years have been really exciting since I had the opportunity to study in an environment rich of brilliant researchers and since I had both the possibility of learning basic tools from every branch of logic and the one of focusing on the issue of algebraic semantic for propositional logics that yield me to the study of the Leibniz hierarchy. From September 2011 I am working on my master thesis, whose I attached a draft, with Professor **** **** in which I develop a categorial generalization of the semantic isomorphism theorem for algebrizable logics.

I would like to join the PhD program of the ILLC because as I think it is a place where the interests that characterized till now my studies, that are algebra and logic from the mathematical side and philosophy of language and formal analysis of natural languages from the philosophical one, are seen as a whole subject. It is for this reason that I kept contact with Professor **** **** that is working on a theme that share both the mathematical and philosophical features I am interested in: the one of inquisitive logic.

Perhaps the best way to explain shortly what is inquisitive logic, is to begin with a philosophical excursus on the motivation that led to its introduction. Traditionally the meaning of a sentence has been identified with its informative content, an option that revealed very fruitful but that is not able to explain the dynamic aspects of language that are not directly concerned with an informative content such as questions or cooperation between two subjects. In order to plug this gap philosophers and semanticists have recently focused on conversation as the fundamental linguistic context proposing to identify the meaning of a sentence with is its potential to update the common ground between the subjects involved in conversation. From this point of view it is clear that question have the same value as assertions, both contributing in different ways, respectively inquisitive and informative, to develop the common knowledge of the subjects involved in conversation.

These philosophical remarks have a natural formal counterpart: the one of inquisitive semantics in which propositions are viewed as proposals to update, possibly in different ways, the common ground. Thank to this approach one can recover, from a mathematical point view, the intuitive difference between sentences with informative and inquisitive contents.

This formalization give rise to inquisitive logic that turns out to be non-classical since the principle of the excluded middle fails to be true in inquisitive contexts. This may suggest that inquisitive logic lies in the near of intuitionistic logic and in fact it is so, both from a formal and from a philosophical point of view: the two logics present a somewhat similar relational and algebraic semantics and both logics are concerned with a notion of information that is growing and with some notion of temporality or states of knowledge.

The aim of the project I would like to join can be summarized in three point: the first is to use correspondence and duality techniques in order to develop the formal study of the intuitive relation between intuitionistic and inquisitive logic pursuing the lines depicted above. The second is yielding a natural abstraction of the notion of inquisitive in order to provide some more general framework for inquisitive logic that could apply also to non-boolean cases, giving rise to an entire class of logics capturing dynamic aspects of language in intrinsicly non-classical contexts. This point would have some philosophical relevance in the sense that if such an abstraction could be obtained, then it would appear clear that the principles of inquisitive logic are independent from the environment in which they originated, as it turned out for other classes of logics, e.g. many-valued logics. The third is to develop more general semantics such as pointfree semantics.

Thank you very much for considering my application and I look forward to hearing from you.